O LevelMathsCambridge (CIE)Exam QuestionsLengths, Areas & VolumesVolume & Surface Area

Volume & Surface Area (Cambridge (CIE) O Level Maths): Exam Questions

Exam code: 4024

5 hours58 questions

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Volume & Surface Area

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1
Sme Calculator3 marks

The diagram shows a prism.

q1-4-6-easy-edexcel-gcse-maths

Work out the volume of the prism.

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2
Sme Calculator3 marks

Here is a triangular prism.

j80Xn1dy_q2-4-6-easy-edexcel-gcse-maths

Work out the volume of this triangular prism.

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3
Sme Calculator2 marks

The diagram shows a prism.

h61o9nj~_q3-4-6-easy-edexcel-gcse-maths

The area of the cross section of the prism is 30 cm2.
The length of the prism is 25 cm.

Work out the volume of the prism.

How did you do?

4
Sme Calculator2 marks
cie-igcse-2020-oct-nov-p4-tz3-q6a

ABCDEFGH is a cuboid.
AB = 8 cm, BC = 5 cm and CG = 11 cm.

Work out the volume of the cuboid.  

.......................................... cm3

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1
Sme Calculator4 marks

A solid cylinder has radius 3 cm and height 4.5 cm.  

Calculate the total surface area of the cylinder.
Give your answer in terms of straight pi.  

................................................ cm2

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2
Sme Calculator2 marks

The volume of a cuboid is 180 cm3.
The base is a square of side length 6 cm.  

Calculate the height of this cuboid.  

....................................... cm

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3
Sme Calculator3 marks

A water tank in the shape of a cuboid has length 1.5 metres and width 1 metre.
The water in the tank is 60 centimetres deep.  

Calculate the number of litres of water in the tank.  

....................................... litres

How did you do?

4
Sme Calculator3 marks
cie-igcse-2018-may-jun-2-p2-q14

The diagram shows a solid cuboid with base area 7 cm2.
The volume of this cuboid is 21 cm3.

Work out the total surface area.

......................................... cm2

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5
Sme Calculator3 marks

Find the volume of a cylinder of radius 5 cm and height 8 cm. Give your answer in terms of straight pi.
Give the units of your answer.

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6
Sme Calculator3 marks
cie-igcse-2019-oct-nov-p4-tz2-q4a

The diagram shows a hemisphere with radius 6 cm.

Calculate the volume.
Give your answer in terms of straight pi.
Give the units of your answer.
[The volume, V, of a sphere with radius r is V equals 4 over 3 straight pi r cubed.]

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7
Sme Calculator1 mark

A cube has side length x cm. The volume of the cube is 1000 cm3.  

Calculate the value of x.  

x = ....................................................

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8
Sme Calculator2 marks
cie-igcse-2018-oct-nov-p4-tz2-q10b

A solid metal cone has radius 10 cm and height 36 cm.

Calculate the volume of this cone.
Give your answer in terms of straight pi.
[The volume, V, of a cone with radius r and height h is  V equals 1 third straight pi r squared h.]  

 

......................................... cm3

How did you do?

9a2 marks
Prism ABCDEFGH with cross-section in for m of a trapezium represented by face ABCD, where the parallel sides BC and AD are labelled 6 and 9 and the perpendicular height AB is labelled 4. The length of the prism DH is labelled 14.

The diagram shows a solid plastic gaming piece in the shape of a prism.
The cross-section of the prism, A B C D, is a trapezium.
A B equals space 4 space cm, B C equals space 6 space cm, A D equals space 9 space cm and D H equals space 14 space cm.

Calculate the area of trapezium A B C D.

......................................... cm squared

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9b2 marks

Calculate the volume of plastic needed to make the gaming piece.
 

......................................... cm cubed

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9c6 marks

Calculate the total surface area of the gaming piece.

......................................... cm squared

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9d2 marks

A mathematically similar gaming piece is also made. The trapezium forming its cross-section has a height of 2 cm instead of 4 cm.

Calculate the total surface area of this gaming piece with a cross-section height of 2 cm.

......................................... cm squared

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1
Sme Calculator4 marks
cie-igcse-2020-oct-nov-p2-tz1-q18

The diagram shows a solid made from a cylinder and a hemisphere, both of radius 7cm.
The cylinder has length 12 cm.

Work out the total surface area of the solid.
Give your answer in terms of straight pi.
[The surface area, A, of a sphere with radius r is A space equals space 4 pi italic space r squared]

 ........................................... cm squared 

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2
Sme Calculator5 marks

A container is made from a cylinder and a cone, each of radius 5 cm.
The height of the cylinder is 12 cm and the height of the cone is 4.8 cm.

cie-igcse-2019-oct-nov-p2-tz3-q221

The cylinder is filled completely with water.
The container is turned upside down as shown below.

cie-igcse-2019-oct-nov-p2-tz3-q222

Calculate the depth, d, of the water.
[The volume, V, of a cone with radius r and height h is V equals 1 third straight pi r squared h.]

d = ............................................. cm

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3a
Sme Calculator4 marks
cie-igcse-2018-oct-nov-p4-tz3-q3b

The diagram shows a solid cylinder and a solid sphere.
The cylinder has radius 3 r and height 8 r.
The sphere has radius r.

Find the volume of the sphere as a fraction of the volume of the cylinder.
Give your answer in its lowest terms.
[The volume, V, of a sphere with radius r is V equals 4 over 3 straight pi r cubed .]

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3b
Sme Calculator4 marks

The surface area of the sphere is 81straight pi cm2.  

Find the curved surface area of the cylinder.
Give your answer in terms of straight pi.
[The surface area, A, of a sphere with radius r is  A equals 4 straight pi r squared.]  

........................................... cm2

How did you do?

4a
Sme Calculator2 marks
q10-specimen-paper1-2025-4024-01-cambridge-o-level-maths-d

The diagram shows a container in the shape of a prism with an open top.
The cross-section of the prism, A B C D, is a trapezium. A B space equals space 14 space cm, C D space equals space 26 space cm and B F space equals space 30 space cm.
The height of the container is 8 space cm.
The area of the cross-section is 160 space cm squared

Calculate the capacity of the container in litres.

...................................... litres

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4b
Sme Calculator6 marks

Calculate the total surface area of the inside of the container.

......................................... cm2

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1
Sme Calculator3 marks

A solid cylinder has radius x cm and height fraction numerator 7 x over denominator 2 end fraction cm.
The surface area of a sphere with radius R cm is equal to the total surface area of the cylinder.  

Find an expression for R in terms of x.
[The surface area, A, of a sphere with radius r is space A equals 4 straight pi r squared.]  

R equals................................................

How did you do?

2
Sme Calculator5 marks

The diagram below shows a solid circular cone and a solid sphere.

cie-igcse-2020-specimen-p4-q10c

The cone has radius 5 x cm and height 12 x cm.
The sphere has radius r cm.
The cone has the same total surface area as the sphere.

Show that  r squared space space equals space 45 over 2 x squared.
[The curved surface area, A, of a cone with radius r and slant height l is A equals pi r l.]
[The surface area, A, of a sphere with radius r is A equals 4 pi r squared.]

How did you do?

3a
Sme Calculator2 marks
cie-igcse-2018-may-jun-3-p4-q7b

The diagram shows three solids.
The base radius of the cone is 6 cm and the slant height is 12 cm.

Show that the total surface area of the cone is 108straight pi cm2.
[The curved surface area, A, of a cone with radius r and slant height l is A equals straight pi r l.]

How did you do?

3b
Sme Calculator4 marks

The radius of the sphere is x cm and the radius of the hemisphere is y cm.
The total surface area of each solid is the same.   

Find the value of x and the value of y.
Give the value of x as a simplified surd.
[The surface area, A, of a sphere with radius r is A equals 4 straight pi r squared.]

x equals..............................................   
   y equals............................................... 

How did you do?